Understanding Keynes on Income, Saving, and Investment.

Keynes covers these topics in chapter 6 of his General Theory. The chapter is very wordy and contains few examples – Keynes was not a good communicator of his ideas. This piece seeks to present his key ideas from chapter 6 in a more user friendly way so as to make them more accessible to a wider audience. A brief case study will be used.

Keynes’s model excludes the foreign sector and thus assumes UK firms operate within a closed economy. Apart from the business and possibly the household sector, Keynes’s model makes no explicit reference to other sectors of the UK economy, eg the government or financial sector.

However, Keynes is correct to make this apparent omission because the trading section of a firm’s traditional income statement is alone relevant to the determination of how much wealth has been created in a period. The remaining sections of a traditional income statement report the revenues associated with the other sectors of the economy, and merely show how the created wealth has been distributed among the factors of production. Keynes calls these remaining costs “factor costs”. These factor costs, eg wages, rent, taxes, interest, and dividends can be associated with suitably chosen sectors, eg households, government, financiers, and/or rentiers. Keynes concentrates on wealth creation, not on how the wealth is distributed between the other sectors. For this reason, this exposition starts with a traditional, widely used and understood trading account before developing it into a value added statement.

Consider the following consolidated trading accounts of the B2B and B2C sectors of the domestic economy. The trading accounts are prepared in traditional format which any accountant would instantly recognise.

Trading Accounts (£k)Consolidated
B2B
Consolidated
B2C
Revenue+1,000+2,000
Opening
inventories
200400
Purchases 01,000
Closing inventories+100+200
Cost of goods sold– 1001,200
Gross profit + 900+ 800

The purchases figures in trading accounts consist entirely of revenue expenditure, eg raw materials, goods for resale, etc. The purchases figure for the consolidated B2B sector is zero because the aggregate purchases of B2B firms will cancel against B2B sales revenue on consolidation. In other words, B2B firms will be selling and buying from each other and, in aggregate, the sector’s purchases and sales will cancel out to zero (unless they import). For this reason, only sales made to B2C firms will be recorded in the B2B sector’s consolidated account. This is why the sales revenue of the consolidated B2B sector is identical to the purchases of the B2C sector. These like items will cancel when the B2B sector is consolidated with the B2C sector. The following table shows the consolidation of the two sectors and the cancellation of the like items:

Trading Accounts (£k)Consolidated
B2B
Consolidated
B2C
AdjustmentB2B consolidated
with B2C
Revenue+ 1,000+ 2,000 – 1,000+ 2,000
Opening
Inventories
200400– 600
Purchases 01,000+ 1,000 0
Closing inventories+ 100+ 200+ 300
Cost of goods sold1001,200+ 1,000– 300
Gross profit + 900+ 800+ 1,700

The above trading accounts can be rearranged so that value added is yielded by the bottom line in place of gross profit. Value Added is what Keynes deemed, in the context of national income accounting, to be income (Y). He rejects using the bottom line (the net profit or net income) of traditional income statements as a relevant measure of income in the context of national income accounting. This is because net profit is calculated after deducting factor costs from gross profit. The factor costs are the revenue of the other sectors of the economy and so will cancel out on consolidation.

The value added statements of the two business sectors are shown below.

Code DescriptionConsolidated
B2B (£k)
Consolidated
B2C (£k)
ARevenue+ 1,000+ 2,000
A1Purchases 0– 1,000
IInventory adjustment100 200
Y Value Added+ 900+ 800

The letters appearing under the code heading are those used by Keynes in his General Theory to denote either a) the category into which an item falls or b) as a specific identifier. For example, closing and opening inventories both fall into the “Investment” category and hence have an I against them. A and A1 are specific identifiers and denote Revenue and Purchases respectively. The inventory adjustment ensures that it is materials used, or goods sold, that is set against revenue, not the purchases figure. So for the B2C sector, raw materials used, or goods sold, £1,200k has been set against revenue.

Value Added Statements can be consolidated using the same rules as with the trading account, i.e., cancel linked items and then aggregate the remaining items, as shown below.

Code DescriptionConsolidated
B2B (£k)
Consolidated
B2C (£k)
Adjustment (£k)Consolidated Value
Added Statement (£k)
ARevenue+ 1,000+ 2,000– 1,000+ 2,000
A1Purchases 0– 1,000+ 1,0000
IInventory adjustment100 200 300
YValue Added+ 900+ 800+ 1,700

Purchases (A1)

In a traditional trading account, the purchases figure (A1) will consist entirely of revenue items. An inventory adjustment is usually required to ensure that unused materials, or unsold goods, from the previous period are set against the current period’s revenue. The inventory adjustment also ensures that unused materials or unsold goods in the current period are carried over to the immediately following period.

Keynes, however, in his General Theory, includes both capital and revenue items within A1. So for Keynes, if a firm makes a one-off purchase of capital equipment from another firm then Keynes would designate the transaction as (A) by the seller and as (A1) by the purchaser. When capital items are included in A1, the purchasing firm’s value added will be understated because A1 will be overstated. An adjustment is necessary to correct for this and this is done via a capital adjustment which will show the part of A1 which is capital expenditure as investment (I).

Capital Adjustments

In his General Theory, Keynes brings up the need to recognise the deterioration of the entrepreneur’s capital equipment in the calculation of value added. He proposes what, in practice, might be an over elaborate calculation for capital consumption. However, his formula is elegant because it also yields how much capital formation has taken place. This calculation is hopefully explained correctly below.

Keynes’s calculation seeks to compare the theoretical value of capital equipment which has been hypothetically mothballed, to the actual value of the same equipment after it has been used in production. His premise is that capital equipment used in production loses value due to use and should have a lower value than identical, well maintained capital equipment that has hypothetically lain idle in the period. His method for determining the capital adjustment, using his notation, is to apply the following formula:

(G – B) – G

where G represents the theoretical end value of capital equipment that has been idle for the period after B has been spent improving it or keeping it in good working condition, and

where G is the actual end value of capital equipment after it has been used in production in the period.

G – B enables the opening valuation of the capital equipment to be determined.

Three possible cases may arise and Keynes’s formula is used below to illustrate.

Case 1: Capital consumption occurs

This occurs when (G – B) > G.

Put simply, this means the closing valuation of the capital equipment is less then the opening valuation. This indicates depreciation through use has occurred.

Example

The theoretical end value (G) of idle equipment was £300,000 after spending £100,000 on idle equipment maintenance (B) during the period. The actual value (G) at the period end was £175,000.

The first step is to insert the relevant figures on the left hand section of the table. The theoretical opening balance can thereby be obtained and transferred to the right side section. The actual closing valuation (given) is then inserted. The capital adjustment (shown in red) is the difference between the actual closing valuation and the theoretical opening valuation.

Equipment idle£kEquipment used£k
Opening valuation (G – B)200Opening valuation200
Maintenance expenditure (B)100Capital consumption(25)
Theoretical
closing valuation (G)
300Actual
closing valuation (G)
175

So in case 1 capital consumption is £25,000 and this amount should be charged to the entrepreneur’s value added statement. It represents disinvestment and should be coded with an I. The accountant’s production unit basis for depreciation may suffice as a reasonable proxy measure consistent with Keynes’s conception of capital consumption.

Case 2: No capital consumption or formation occurs

This occurs when (G – B) = G

The theoretical end value (G) of idle equipment was £300,000 after spending £100,000 on idle equipment maintenance (B) during the period. The actual value at the period end was £200,000.

Equipment idle£kEquipment used£k
Opening valuation (G – B)200Opening valuation200
Maintenance expenditure (B)100Capital consumption0
Theoretical
closing valuation (G)
300Actual
closing valuation (G)
200

In this case, no capital consumption occurred so no charge to the value added statement is required in respect of capital consumption.

Case 3: Capital formation occurs.

This occurs when (G’ – B) < G.

Put simply, this means the closing valuation is higher than the opening valuation. This indicates that capital equipment has been acquired during the period

Example

The theoretical end value (G) of idle equipment was £300,000 after spending £100,000 on idle equipment maintenance (B) during the period. The actual value at the period end was £450,000.

Equipment idle£kEquipment used£k
Opening valuation (G – B)200Opening valuation200
Maintenance expenditure (B)100Capital formation250
Theoretical
closing valuation (G)
300Actual
closing valuation (G)
450

In this case, the firm may have been increasing its capital equipment by its own labour or by purchasing it from another firm. When capital equipment is produced in-house, the wages and salaries of that part of the labour force assigned to the production of the capital equipment will have been capitalised (i.e., included in the actual valuation). Capital equipment produced by an individual firm for its own use should be recognised in the individual’s firm’s value added statement as investment expenditure and should be coded as I.

In the value added statements that follow the capital adjustment from case 1 above has been incorporated into B2B’s results. The capital adjustment from case 3 has been incorporated in B2C’s results.

CodeDescriptionB2BB2CAdjustmentConsolidated
ARevenue1,0002,000(1,000)2,000
A1Purchases0(1,000)1,0000
IInventory adjustment(100)(200)(300)
ICapital adjustment(25)250225
Y
Value Added8751,0501,925

Apart from items on the edges, eg Suplementary Costs, income determination under Keynes’s scheme is concluded.

Consumption Expenditure (C)

The revenue figure of £2,000 in the consolidated column represents the total sales made by B2C firms to consumers. This is because all B2B sales figures have been eliminated by the consolidation process. The revenue figure in the consolidated value added statement thus represents consumption expenditure (C). Using Keynes’s notation consumption expenditure can be otained from the total of A minus the total of A1. The consolidated revenue, as shown above, is the result of the sum of A minus the sum of A1 .

Saving (S)

Saving is by (strict) definiton equal to income minus consumption. The consolidated value added figure of £1,925 represents aggregate income. Subtracting the aggregate consumption expenditure figure of £2,000, a negative figure for aggregate saving (S) of – £75 is obtained. It is no accident that the aggregate saving figure is equal to the aggregate investment figure shown in the consolidated value added statement.

User cost (U)

Keynes appears to set much store by this figure. The user cost repesents the costs that have been consumed (as distinct from being incurred). It is the sum of materials used/goods sold (A1 – inventory adjustments) and capital adjustments (capital consumption – capital formation). The user cost (U) can (theoretically) be negative in which case it is added to revenue. The user cost (U) can be calculated from A1 – I. It is most meaningful at individual firm level since A1 becomes zero on consolidation. The user cost for the B2C sector can be seen to be equal to £950 (£1,000 + £200 – £250). Value Added, which is now the accepted definition of income for national income determination, can be obtained from subtracting an individual firm’s user cost from the firm’s revenue (A) (eg, £2,000 – £950 = £1,050).

Investment Expenditure (I)

This is equal to the inventory adjustment plus the capital adjustment. If the closing inventories are higher than the opening inventories then investment will have occured. If the closing inventories are lower then disinvestment will have occurred.

Capital consumption decreases the period’s investment. Capital formation will increase investment.

Positive investment increases value added.

Summary

The above exposition is a condensed summary of chapter 6 of Keynes’s General Theory. The exposition is intended to make accessible the important material in that difficult-to-read chapter to a wider, less specialised readership, eg accountancy and business studies students. The more marginal topics in that chapter have not been given much weight in this exposition.

Chapter 6 shows that income for national income accounting is most closely aligned to the gross profit figure which is found in traditional commercial income statements. Gross profit figures are augmented with capital adjustments to arrive at value added. Keynes’s proposed formula for capital adjustments has been unpacked so as to make it more understandable. The resulting income is known as value added.

Keynes’s analysis has its focus on the creation of wealth. The distribution of wealth to the other sectors of the economy does not figure in his analysis. However, the government does prepare analyses to show “who got what” via the income approach to GDP determination.

Keynes shows how investment is equal to saving by adhering strictly to the defintion of saving as being equal to Income minus Consumption. In the consolidated value added statement value added (income) has been determined as £1,925k and consumption expenditure as £2,000k. Hence saving is – £75k.

Keynes’s analysis assumes a closed economy. The introduction of a foreign sector would appear to render some of his analysis inadequate.


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